Quarter 8-cubic honeycomb

quarter 8-cubic honeycomb
(No image)
Type	Uniform 8-honeycomb
Family	Quarter hypercubic honeycomb
Schläfli symbol	q{4,3,3,3,3,3,3,4}
Coxeter diagram	=
7-face type	h{4,3⁶}, h₆{4,3⁶}, {3,3}×{3^2,1,1} duoprism {3^1,1,1}×{3^1,1,1} duoprism
Vertex figure
Coxeter group	${\tilde {D}}_{8}$ ×2 = [[3^1,1,3,3,3,3,3^1,1]]
Dual
Properties	vertex-transitive

In seven-dimensional Euclidean geometry, the quarter 8-cubic honeycomb is a uniform space-filling tessellation (or honeycomb). It has half the vertices of the 8-demicubic honeycomb, and a quarter of the vertices of a 8-cube honeycomb.^[1] Its facets are 8-demicubes h{4,3⁶}, pentic 8-cubes h₆{4,3⁶}, {3,3}×{3^2,1,1} and {3^1,1,1}×{3^1,1,1} duoprisms.

Notes

Kaleidoscopes: Selected Writings of H. S. M. Coxeter, edited by F. Arthur Sherk, Peter McMullen, Anthony C. Thompson, Asia Ivic Weiss, Wiley-Interscience Publication, 1995, ISBN 978-0-471-01003-6 [1]
- (Paper 24) H.S.M. Coxeter, Regular and Semi-Regular Polytopes III, [Math. Zeit. 200 (1988) 3-45] See p318 [2]
Klitzing, Richard. "7D Euclidean tesselations#7D".

v t e Fundamental convex regular and uniform honeycombs in dimensions 2-9
Space	Family	${\tilde {A}}_{n-1}$	${\tilde {C}}_{n-1}$	${\tilde {B}}_{n-1}$	${\tilde {D}}_{n-1}$	${\tilde {G}}_{2}$ / ${\tilde {F}}_{4}$ / ${\tilde {E}}_{n-1}$
E2	Uniform tiling	{3^[3]}	δ₃	hδ₃	qδ₃	Hexagonal
E3	Uniform convex honeycomb	{3^[4]}	δ₄	hδ₄	qδ₄
E4	Uniform 4-honeycomb	{3^[5]}	δ₅	hδ₅	qδ₅	24-cell honeycomb
E5	Uniform 5-honeycomb	{3^[6]}	δ₆	hδ6	qδ6
E6	Uniform 6-honeycomb	{3[7]}	δ7	hδ7	qδ7	222
E7	Uniform 7-honeycomb	{3[8]}	δ8	hδ8	qδ8	133 • 331
E8	Uniform 8-honeycomb	{3[9]}	δ9	hδ9	qδ₉	152 • 251 • 521
E9	Uniform 9-honeycomb	{3^[10]}	δ₁₀	hδ₁₀	qδ₁₀
E10	Uniform 10-honeycomb	{3^[11]}	δ₁₁	hδ₁₁	qδ₁₁
En-1	Uniform (n-1)-honeycomb	{3[n]}	δn	hδn	qδn	1k2 • 2k1 • k21